Apparatus and method for constraining the value of feedback filter tap coefficients in a decision feedback equalizer
View Patent ↗An apparatus and method is disclosed for reducing error propagation in a decision feedback equalizer by constraining the values of feedback filter tap coefficients in a feedback filter of the decision feedback equalizer. The feedback filter tap coefficients that are constrained are calculated using a constraint cost function and a related constraint function. The constraint condition of the present invention reduces error propagation in a decision feedback equalizer by preventing error from circulating in a feedback loop of a feedback filter within the decision feedback equalizer.
1. An apparatus for calculating a plurality of feedback filter tap coefficients in a feedback filter of a decision feedback equalizer, wherein said apparatus limits a magnitude of each of the plurality of feedback filter tap coefficients to a total energy of the feedback filter tap coefficients to reduce error propagation in said decision feedback equalizer, and wherein said apparatus calculates each of the plurality of feedback filter tap coefficients using:
g
n
k
+
1
=
g
n
k
+
μ
e
k
a
k
-
n
-
λ
∂
J
∂
g
n
where
g
n
k
is a feedback filter tap coefficient at time k, μ is an adaptation speed constant, e k is an error term, α k−n is a value of feedback filter tap data in said feedback filter at time k, J is a constraint cost function, and λ is a small positive constant.
2. The apparatus of claim 1 , wherein said cost constraint function J is given by:
J=M ( g n ) 2 if M ( g n )>0
J= 0 if M ( g n )≦0
where M(g n ) is a constraint function and where g n is a feedback filter tap coefficient.
3. The apparatus of claim 2 , wherein said constraint function M(g n ) is given by:
M
(
g
n
)
=
∑
n
=
0
N
-
1
g
n
2
-
D
where D is said total energy of said feedback filter tap coefficients.
4. The apparatus of claim 2 , wherein said constraint function M(g n ) is given by:
M ( g n )=| g n |−D
where D is said total energy of said feedback filter tap coefficients.
5. The apparatus of claim 1 , wherein said apparatus calculates a forward filter tap coefficient for a forward filter using:
f
n
k
+
1
=
f
n
k
+
μ
e
k
r
k
-
n
-
λ
∂
J
∂
f
n
where
f
n
k
is a forward filter tap coefficient at time k, μ is an adaptation speed constant, e k is an error term, r k−n is a value of forward filter tap data in said forward filter at time k, J is a constraint cost function, and λ is a small positive constant.
6. A digital receiver system comprising an apparatus for calculating a plurality of feedback filter tap coefficients in a feedback filter of a decision feedback equalizer, wherein said apparatus limits a magnitude of each of the plurality of feedback filter tap coefficients to a total energy of said feedback filter tap coefficients to reduce error propagation in said decision feedback equalizer and wherein said apparatus calculates each of the plurality of feedback filter tap coefficients using:
g
n
k
+
1
=
g
n
k
+
μ
e
k
a
k
-
n
-
λ
∂
J
∂
g
n
where
g
n
k
is a feedback filter tap coefficient at time k, μ is an adaptation speed constant, e k is an error term, a k−n is a value of feedback filter tap data in said feedback filter at time k, J is a constraint cost function, and λ is a small positive constant.
7. The digital receiver system of claim 6 , wherein said cost constraint function J is given by:
J=M ( g n ) 2 if M ( g n )>0
J= 0 if M ( g n )≦0
where M(g n ) is a constraint function and where g n is a feedback filter tap coefficient.
8. The digital receiver system of claimed 7 , wherein said constraint function M(g n ) is given by:
M
(
g
n
)
=
∑
n
=
0
N
-
1
g
n
2
-
D
where D is said total energy of said feedback filter tap coefficients.
9. The digital receiver system of claim 7 , wherein said constraint function M(g n ) is given by:
M (i g n )=| g n −D
where D is said total energy of said feedback filter tap coefficients.
10. The digital receiver system of claim 6 , wherein said apparatus calculates a forward filter tap coefficient for a forward filter using:
f
n
k
+
1
=
f
n
k
+
μ
e
k
r
k
-
n
-
λ
∂
J
∂
f
n
where
f
n
k
is a forward filter tap coefficient at time k, μ is an adaptation speed constant, e k is an error term, r k−n is a value of forward filter tap data in said forward filter at time k, J is a constraint cost function, and λ is a small positive constant.
11. A method for reducing error propagation in a decision feedback equalizer, the method comprising:
calculating a plurality of feedback filter tap coefficient in a feedback filter in said decision feedback equalizer; and
limiting a magnitude of each of the plurality of feedback filter tap coefficients to a total energy of the feedback filter tap coefficients, wherein said calculating said feedback filter tap coefficients comprises calculating a feedback filter tap coefficient using:
g
n
k
+
1
=
g
n
k
+
μ
e
k
a
k
-
n
-
λ
∂
J
∂
g
n
where
g
n
k
is a feedback filter tap coefficient at time k, μ is an adaptation speed constant, e k is an error term, a k−n is a value of feedback filter tap data in said feedback filter at time k, J is a constraint cost function, and λ is a small positive constant.
12. A method as claimed in claim 11 , wherein said cost constraint function J is given by:
J=M ( g n ) 2 if M ( g n )>0
J= 0 if M ( g n )≦0
where M(g n ) is a constraint function and where g n is a feedback filter tap coefficient.
13. A method as claimed in claim 12 , wherein said constraint function M(g n ) is given by:
M
(
g
n
)
=
∑
n
=
0
N
-
1
g
n
2
-
D
where D is said total energy of said feedback filter tap coefficients.
14. The method of claim 12 , wherein said constraint function M(g n ) is given by:
M ( g n )=| g n |−D
where D is said total energy of said feedback filter tap coefficients.
15. The method of claim 11 , further comprising:
calculating a forward filter tap coefficient for a forward filter using:
f
n
k
+
1
=
f
n
k
+
μ
e
k
r
k
-
n
-
λ
∂
J
∂
f
n
where
f
n
k
is a forward filter tap coefficient at time k, μ is an adaptation speed constant, e k is an error term, r k−n is a value of forward filter tap data in said forward filter at time k, J is a constraint cost function, and λ is a small positive constant.
16. A computer executable process, stored on a computer readable storage medium, for reducing error propagation in a decision feedback equalizer, the process comprising:
calculating a plurality feedback filter tap coefficient in a feedback filter in said decision feedback equalizer; and
limiting a magnitude of each of the plurality of feedback filter tap coefficients to a total energy of the feedback filter tap coefficients, wherein said calculating said feedback filter tap coefficients comprises calculating a feedback filter tap coefficient using:
g
n
k
+
1
=
g
n
k
+
μ
e
k
a
k
-
n
-
λ
∂
J
∂
g
n
where
g
n
k
is a feedback filter tap coefficient at time k, μ is an adaptation speed constant, e k is an error term, a k−n is a value of feedback filter tap data in said feedback filter at time k, J is a constraint cost function, and λ is a small positive constant.
17. The computer executable process of claim 16 , wherein said cost constraint function J is given by:
J=M ( g n ) 2 if M ( g n )>0
J= 0 if M ( g n )≦0
where M(g n ) is a constraint function and where g n is a feedback filter tap coefficient.
18. The computer executable process of claim 17 , wherein said constraint function M(g n ) is given by:
M
(
g
n
)
=
∑
n
=
0
N
-
1
|
g
n
|
2
-
D
where D is said total energy of said feedback filter tap coefficient.
19. The computer executable process of claim 17 , wherein said constraint function M(g n ) is given by:
M ( g n )=| g n |−D
where D is said total energy of said feedback filter tap coefficients.
20. The computer executable process of claim 16 , further comprising:
calculating a forward filter tap coefficient for a forward filter using:
f
n
k
+
1
=
f
n
k
+
μ
e
k
r
k
-
n
-
λ
∂
J
∂
f
n
where
f
n
k
is a forward filter tap coefficient at time k, μ is an adaptation speed constant, e k is an error term, r k−n is a value of forward filter tap data in said forward filter at time k, J is a constraint cost function, and λ is a small positive constant.